A second regime (II) emerges as \(k\)  approaches the critical value, where a much faster and deeper liquid cavity develops across the bubble and, ensuing from diminished capillary forces, further delays to pinch-off are recorded. These delays lead to the entrapment of the first drop in regions approaching the bubble nose in the axial direction, promptly leading to its rupture, as illustrated at \(\tilde{t} = 5.32\)  in figure REF (c, middle). Following a series of end-pinching events, the liquid cavity undergoes several instances of escapes of pinch-off, in conjunction with a surge of surface capillary waves across its domain, and a radial growth that gives rise to a large bulbous end (see \(\tilde{t} = 8.86\) ). These mechanisms are closely related to the intricate phenomena stemming from retracting liquid filaments, as addressed in [1]}, [2]}. This substantial growth causes the liquid cavity to swiftly burst the interface near the channel walls, thereby fully separating the original bubble into two individual entities. Notably, the fate of the newly-formed small entity located further down the stream-wise direction mirrors that of the original bubble as new instances of encapsulation are observed. These bursting mechanisms are wholly in line with the observations of [3]} for close-to-spherical bubbles under similar conditions of \(k\)  and \(Ca\)  (see figure 16 of this reference) and the reports of [4]} for contraction/expansion channels with a viscoelastic liquid phase. Following this busting, capillary forces will attempt to minimise surface area by closing the openings of the newly-formed bubbles.
